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  1. Science in China Series A: Mathematics
  2. Science in China Series A: Mathematics : Volume 54
  3. Science in China Series A: Mathematics : Volume 54, Issue 11, November 2011
  4. Freeness and matrix decompositions
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Science in China Series A: Mathematics : Volume 60
Science in China Series A: Mathematics : Volume 59
Science in China Series A: Mathematics : Volume 58
Science in China Series A: Mathematics : Volume 57
Science in China Series A: Mathematics : Volume 56
Science in China Series A: Mathematics : Volume 55
Science in China Series A: Mathematics : Volume 54
Science in China Series A: Mathematics : Volume 54, Issue 12, December 2011
Science in China Series A: Mathematics : Volume 54, Issue 11, November 2011
Leibniz seminorms and best approximation from C*-subalgebras
Progress in noncommutative function theory
The tracial topological rank of certain C*-algebras
Freeness and matrix decompositions
A modified version of free orbit-dimension of von Neumann algebras
Injectivity and projectivity in analysis and topology
Operator valued frames and structured quantum channels
Dirac cohomology and Dirac induction
Positive combinations of projections in von Neumann algebras and purely infinite simple C*-algebras
Applications of Orlicz-Hardy spaces associated with operators satisfying Poisson estimates
On some mathematical aspects of the Heisenberg relation
Characterization of Lie multiplicative isomorphisms between nest algebras
Paving small matrices and the Kadison-Singer Extension Problem II—computational results
Lipschitzness of *-homomorphisms between C*-metric algebras
Volterra operator, area integral and Carleson measures
Deformation quantization and noncommutative black holes
Science in China Series A: Mathematics : Volume 54, Issue 10, October 2011
Science in China Series A: Mathematics : Volume 54, Issue 9, September 2011
Science in China Series A: Mathematics : Volume 54, Issue 8, August 2011
Science in China Series A: Mathematics : Volume 54, Issue 7, July 2011
Science in China Series A: Mathematics : Volume 54, Issue 6, May 2011
Science in China Series A: Mathematics : Volume 54, Issue 5, May 2011
Science in China Series A: Mathematics : Volume 54, Issue 4, April 2011
Science in China Series A: Mathematics : Volume 54, Issue 3, March 2011
Science in China Series A: Mathematics : Volume 54, Issue 2, February 2011
Science in China Series A: Mathematics : Volume 54, Issue 1, January 2011
Science in China Series A: Mathematics : Volume 53
Science in China Series A: Mathematics : Volume 52
Science in China Series A: Mathematics : Volume 51
Science in China Series A: Mathematics : Volume 50
Science in China Series A: Mathematics : Volume 49
Science in China Series A: Mathematics : Volume 48
Science in China Series A: Mathematics : Volume 47
Science in China Series A: Mathematics : Volume 46
Science in China Series A: Mathematics : Volume 45
Science in China Series A: Mathematics : Volume 44
Science in China Series A: Mathematics : Volume 43
Science in China Series A: Mathematics : Volume 42
Science in China Series A: Mathematics : Volume 41
Science in China Series A: Mathematics : Volume 40

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Freeness and matrix decompositions

Content Provider Springer Nature Link
Author Ge, Liming Shen, Junhao
Copyright Year 2011
Abstract If a semicircular element and the diagonal subalgebra of a matrix algebra are free in a finite von Neumann algebra (with respect to a normal trace), then, up to the conjugation by a diagonal unitary element, all entries of the semicircular element are uniquely determined in the sense of (joint) distribution. Suppose a selfadjoint element is free with the diagonal subalgebra. Then, in the matrix decomposition of the selfadjoint element, any two entries cannot be free with each other unless the selfadjoint element is semicircular. We also define a “matricial distance” between two elements and show that such distance for two free semicircular elements in a finite von Neumann algebra is nonzero and independent of the properties of the von Neumann algebra.
Starting Page 2309
Ending Page 2327
Page Count 19
File Format PDF
ISSN 16747283
Journal Science in China Series A: Mathematics
Volume Number 54
Issue Number 11
e-ISSN 18691862
Language English
Publisher SP Science China Press
Publisher Date 2011-11-04
Publisher Place Heidelberg
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword von Neumann algebra factor semicircular element joint distribution Applications of Mathematics
Content Type Text
Resource Type Article
Subject Mathematics
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